The shutters will come down on all 285 Rumbelows branches by the end of April. In addition the 36 Fona shops, an experimental concept offering rent-to-own schemes on items such as televisions and videos, will also close, bringing total job losses to 2,900.
Rumbelows has been losing £12m a year and has never made a profit in its 24 years of existence.
Thorn EMI's chairman, Sir Colin Southgate, said: "It's very sad, and all the Rumbelows staff have worked terrifically hard. But we've been testing new ideas for seven years. They haven't worked, so you have to make a decision and get it out of the way."
Sir Colin said the industry was over-supplied and that Rumbelows was only a small player.
Experts said the stores were in the wrong place selling too narrow a range of goods from premises too small for their purpose. Clive Vaughan of retail consultants Verdict Research said: "Rumbelows was not big enough to take on Dixons and was trying to sell both brown goods and white goods in stores not big enough to stock the ranges offered by the out-of-town superstores. It was left like a beached whale."
Rumbelows started life in 1971 when Thorn acquired an Essex and Hertfordshire group of shops called Sidney Rumbelow's. In spite of constant re-structuring, the business always struggled and is estimated to have lost a total of £80m over the last 10 years.
The closure of the chain will cost Thorn EMI a total of £116m, of which £56.7m relates to property and other fixed-asset write-offs. A further £34m will be allocated for redundancies.
The company said it would concentrate its energies in the high street on Radio Rentals and the fledgeling Crazy George chain.
Crazy George stores offer rent-to-own schemes on electrical appliances to so-called cash-constrained customers who have no other access to credit. Five such branches exist (the first two are already making a profit) but Thorn plans a chain of up to 120.
The Labour Party pounced on the Rumbelows closure as an indication of Britain's fragile economic recovery. Ian McCartney, shadow employment minister, described it as "a hammer-blow to any supposed feelgood factor".
The shopworkers' union Usdaw said it had not been consulted about the Rumbelows decision and would seek a meeting with Thorn EMI to try to ensure good severance terms.
Though Thorn EMI's shares slipped 12p to 1,037p, City analysts welcomed the move saying it would take some capacity out of a crowded market. Dixons, which remained committed to the high street, was one group that stood to benefit, they said.
News of the Rumbelows closure came as Thorn EMI announced third-quarter results showing that, even including the dismal Rumbelows performance, group pre-tax profits increased by 25 per cent to £334m on sales up slightly to £3.4bn in the nine months to 31December.
The record label EMI boosted profits by 19 per cent to £252m, and the HMV chain of record stores more than doubled profits to £14m.